we have a 2004 gmc envoy with dule climate control one side will not blow cold it blows air just not cold when the ac is turned on

You have a bad actuator in the dash. There are two the one that contols the side that is not working is at fault. Of course it could be wiring or the control head but those are the unlikely options actuators fail quite oftenn.

Is the compressor engaging? when you switch it to a/c does the engine start laboring from the extra requirement? -or- is it simply the fan what will only blow on one speed? regardless of selection?

its blow hot air from the left side and cold on the right side

why is it blowing hot air on the left side when the air/con is on?

04 gmc envoy cuz need full heat left side hot right side cold what's the problem